Find the sides of a rectangle if its perimeter is 106 cm and its area is 646 cm ^ 2.

We have a rectangle. The perimeter of the rectangle is 106 cm, the area is 646 cm². Find the sides of the rectangle.

Let’s introduce variables. Let x be one side of the rectangle and y the other. Let’s compose and solve a system of two equations with two unknowns:

x + y = 53;

x * y = 646;

Express the variable y in the first equation and substitute it in the second:

y = 53 – x;

x * (53 – x) = 646.

53 * x – x ^ 2 – 646 = 0;

x ^ 2 – 53 * x + 646 = 0;

D = 2809 – 2584 = 225;

x1 = (53 + 15) / 2 = 34;

x2 = (53 – 15) / 2 = 19.

We got two sides of the rectangle: 34 cm and 19 cm.